Background: The relevance of developing mental activity for mastering geometric concepts relates to the change in paradigmatic foundations taking place in modern education. Such a change is associated with the recognition of a schoolchild as a subject of educational and cognitive activity, the initiator of own activity. Objective: The authors attempted to describe a model of a didactic system for developing active usage of geometric concepts in the process of teaching geometry to mathematically gifted schoolchildren in 10-11 grades. The authors also used the GeoGebra dynamic system as a component of the electronic educational environment (EEE). The objective is achieved by characterizing the architecture of the system model, which evokes active usage of geometric concepts within schoolchildren in learning situations; substantiating psychodidactic conditions for the effective development of this activity using the GeoGebra dynamic system; and defining levels, criteria, and indicators of development. Methods: A specially organized educational activity in EEE and a developed system of tasks within the framework of the elective course "Problems of solid geometry and computer graphics" for 10-11 graders represent a didactic means of developing the activities related to figurative-spatial methods of information coding. Findings: The authors described a didactic system model for mastering geometric concepts in figurative structures in the process of teaching geometry to 10- 11 graders using the GeoGebra dynamic system. Conclusions: Fostering schoolchildren's mastering of geometric concepts in figurative structures occurs under the direct influence of teaching. However, this process is complex and internally contradictory. The structure of this kind of activity contains actions of different nature.